Mossberg 500/535 with a combo barrel set. You can buy a mossberg 500 with a smoothbore single bead for small game/fowl, a smoothbore barrel with rifle sights for turkey ( prolly good for yotes too) and a rifled slug barrel for deer. All for 500 dollars. That being said, 9.9 times out of ten quality is directly related to the cash you spend, so a 500 dollar pump gun with 3 barrels generally will not function as well as a pump gun that cost 500 with one barrel. Remington also makes a similar combination in the 870, but at slightly more money.

I agree with above Mossberg is the way to go.

Agreed with NolanOsborne answer above and A + 1 for you gentlemen!!!

I also have a Mossberg 535 and it shoots great and chambered for anything you'll need. However, I have grown more aware of how much play there is in the forestock, and a previous query on this site had others stating the same. Small consideration compared to everything else, but something that's caught my attention.

mossberg 500!

Remington 870, you can go wrong with it!!!

Something that shoots consistent tight patterns, is comfortable to shoot and hold ( consider length of pull and recoil etc) and well camouflaged. A dedicated turkey canon would typically have a shorter barrel ( mine is 24, no problems waterfowling or anything else with it, though a longer barrel seems to swing a bit nicer) and would TYPICALLY have a 3 1/2 inch chamber. I think if you cant kill em with a three, you probably shouldn't be shooting at em, but thats just my two cents.
Some people choose to use optics, either a scope or a reddot type sight. Either an 870, or a mossberg turkey is probably a good buy. Hope that helps